What got the whole ladder-of-fifths theory going for Russell was: listening to various voicings of M13 (Major/Ionian) and M13#11 (Lydian) side-by-side, hearing a fundamentaly different posture in each, and asking "Why?".

That's a good disposition for anyone to adopt who hopes to grapple with the mysteries of tonality and the qualities of consonant/dissonant, in/out, smooth/rouph, and so on, that we all experience and enjoy in both written/recorded music and idle play at our instrument.

However, as many readers of his book can attest to, we also ask "Why?" when it comes to what our ears encounter at the 8th tone in that ladder. It is not an incremental outgrowth, a logical continuation of a pattern begun in the ladder, and Russell puts this tone LAST in the sequence of tones that can expand the basic resources of the Lydian scale.

In addition to this, there is the concern even WITHIN the limits of the 7-tone scale, that the major third is arguably MORE in unity with the tonic than even the M2 or M6, which the ladder theory also does not agree with.

For me, the solution lies in looking deeper into the OS than just the 3rd partial (responsible for the P5 interval and the intire Pythagorean concept of stacking fifths), and instead recognizing that the OS contains a pattern projected by every periodic sound source, consisting of more than just one interval.

A practice recommended and utilized by modern composer/theorist W.A. Mathieau, as well as by theorist Lehonard Euler, is to graphically represent certain partials of the oS in a way that makes their relationship to the tonic and to each other visibly evident.

For example, you draw a dot representing the tonic (on graph paper, for example). A dot to the right of it represents the 3rd partial and the interval it introduces, the perfect fifth. To the right of it, you draw another dot, representing 3 times that number, or 9, the 9th partial. You can graphically see the relationship that the 9th partial, or M2/M9, has to both the tonic and to the P5. You do likewise several times until you have a row representing basically a ladder of fifths:

1 ... 3 ... 9 ... 27 ... 81 and so on.

(representing intervals:

1 ... P5 ... M2 ... M6 ... M3 etc.....)

However, since the 5th partial is responsible for our sense of major third, you draw a dot representing it, now ABOVE the tonic.

5 1... 3 ... 9 ...27 ... 81

(representing intervals:

M31 ... P5 ... M2 ... M6 ... M3 )

Since, in the OS, a partial exists that has that same relationship to the 3rd partial, you include it, the 15th partial, which makes a M7 interval to the tonic. Just like the first row, you can continue the row, including the 45th partial, and so on.

5 ... 15... 45... 1351 ..... 3 .....9 .... 27 .... 81

(representing intervals:

M3 ... M7 ... #4 ... #11 ..... P5 ..... M2 .... M6 .... M3 )

The relationships are clear, whether you write the actual partial number, or just draw a dot, knowing the relationship it has to the tonic an surrounding tones.

You'll notice that in this arrangement, you SEE exactly what you HEAR: a P5 is "close" to the tonic, a M9/M2 is a little farther, the M6 is farther yet, but the M3 - unless accompanied by the aforementioned tones, which would support an 81st partial identity - is CLOSER to the tonic in relationship than either of the previous two tones.

The M7 (having the ratio of the 15th partial) is again more distant, and likewise the #4 (having the ratio of the 45th partial), is more distant still.

The next tone in the series is quite distant indeed, and as we'll see shortly, has a different "version" that is "closer" to the tonic.

If we were to continue in the "ladder of fifths" sequence, we would have a tone that is a #5 to the tonic - much "closer" sounding by Russells, or probably anyone's estimation, than the #1/b2 we just looked at.

Again, the OS itself, and our method of graphing it, can account for this. A M3 above the 5th partial, is the 25th partial (5x5=25). Let's graph it, and see how it relates to the tonic in our "close-to-distant" reconing:

25 5 ... 15... 45... 1351 ... 3 ....9 .... 27

(representing intervals:

M3 ... M7 ... #4 ... #1 1 ..... P5 .... M2 .... M6 )

You can, of course, fill in more tones, the 75th partial (#2/m3), the 225th partial (#6/b7), and so on.

Now, obviously, we don't audibly HEAR all these partials referenced here. However, since each and ever complex periodic waveform projects more or less this logarithmic pattern up to infinity, and our ears apparently are built to respond to this pattern in immediate ways, the relationships and ratios found within the OS are something we intuitively relate to and use to judge/hear/interpret combinations of tones, as we use our unique human gift to percieve and appreciate sound art (music).

You'll notice, then, that the tones that sound more OUT with respect to the tonic, are in fact more distant in their relationship to it. They come about by more complex means than the P5 and M3 do, although they arrise by multiples/compounds of those simple ratios first encountered in the early partials.

Now, this is chapter one. There's much more to follow, and many implications for comparison to the LCC, as well as for day-to-day use by the practicing musician.

An "Interval Vector" is a list of six numbers which summarizes the interval content in a PC Set. With a little experience, you will be able to get a sense for how a PC Set sounds when you see its interval vector. Further, once you know the interval content of a PC Set, you will also be able to manipulate the sound of the PC Set by inversion and octave displacement of pitches to emphasize certain intervals over others.

joegold wrote: "I'm guessing that you already realize this, but it's not evident from your post that you're aware that the 81st partial of your fundamental (marked as an octave double of the M3 interval above the fundamental) is not an exact octave double of the fundamental's 5th partial (which you also marked as being a M3 interval). "

Yes, I do realize that they are not the same ratio. The 5th partial four octaves higher is the 80th partial, so you get the 81:80 difference ratio, or 'syntonic comma'. My inclusion of the 81st partial in the diagram was not meant to suggest that it is equivalent to the 5th partial M3, but to show exactly what you yourself realize: that the OS often provides more than one "version" of an interval, and while both may be legitimate depending on the circumstances, one is always, by both objective and subjective reckoning, "closer" to, or more directly related to, the tonic. This will be very key in some of the forthcoming development of this whole idea.

Hopefully this is no longer puzzling to you.

joegold wrote: "here you are breaking from the way that Mathieu himself introduces this note into the extended "key". Ditto for your method of introducing the b3 and the b7, compared to Mathieu's techniques/ideas. "

That's right. I am not just regurgitating what I read somewhere. Mathieu's intent was not the same as Russell's - to vertically account for all chords and find some unifying factor for chords and scales. I don't introduce these as Mathieu's ideas, but as my own, influenced very much by both himself and Russell. There is no Mathieu vs. Russell suggestion here, and there won't be. (nor is this strachs vs. Russell I might add)

As to the b3 and b7 - I am not suggesting that partials 75 and 225 are "nature's" way of handing us the m3 and m7 intervals. I'm showing that "versions" of these intervals exist as overtones of the fundamental, in the same 'network' of relationships that are prototyped by the major triad and the more familiar expansions of it (adding M7ths and 9ths and the like), and are not at odds with or 'out of alignment' with the major triad, or the Lydian scale. I'm showing this within the context of showing why (I think) the M3 sounds more DIRECTLY related to the tonic than the M2 or M6, and why the #5 also sounds more DIRECTLY related to the tonic than the b2 - namely, that they (the M3 and #5) have a simpler, "closer" tonal relationship with the tonic than do intervals that the "ladder" would claim are "closer", or on a lower rung of the ladder. So, I'm demonstrating that this is an ALTERNATE take on the unity of the Lydian scale, which answers the shortcomings of the "ladder of fifths" theoretical model, and that this can be visually represented in a way agrees with the sound of these intervals.

joegold wrote: "I don't really see how this accounts for the WOTG"

That's because I'm not trying to account for the WOTG. Since I see the WOTG as being at odds with the ladder theory anyway, I'm trying to arrive at a more objective viewpoint of things.

joegold wrote: "Mathieu also extends the horizontal spine of pure 5ths to the left of the tonic and he extends the vertical spine of pure M3's below the tones of the horizontal spine of 5ths. "

Yes. And I'm getting to that. I ended my post by stating this was "chapter one". Rather than supplying more than can be digested in one sitting, I thought I'd break it up a bit. It was an introduction from which I will develop what are, to me, the natural outgrowths of these ideas.

joegold wrote: "the augmented 7th interval (partial #2025) is not enharmonically equivalent to an octave double of the tonic, as it would be in 12TET"

RIght. And that's one of the big realizations I've had in considering all of this: there IS no symmetry in the OS. There IS no circle in the OS. 12TET is a man-made construct with an objective that is entirely HORIZONTAL (the ability to play in DIFFERENT keys and migrate between them on an instrument which is consequently only capable of approximating the harmonies available in a single OS), and therefore is not a suitable yardstick (including the ladder itself) with which to evaluate VERTICAL harmony. Rather, the proportions and relationships that exist within a SINGLE OS are the yardstick for this endeavor. The circle, and therefore the ladder as well, are of great use in HORIZONTAL reckoning, but not for explaining VERTICAL structures such as chords.

joegold wrote: "Or am I missing something?"

The only thing you were missing is that I'm not trying to find a way to justify the WOTG. I found a way to explain (what to me seems like a very sound viewpoint regarding) why the b2 is more "out" than the rest of the "out" tones in the LCS. In the process, I've (unfortunately, from a certain perspective) convinced myself that the "oneness" or "unity" of the Lydian scale is not about a ladder, but about all of the intervals belonging to a pattern that is present in the OS of the tonic. That pattern involves more than just the 3rd partial, but also the 5th partial, and many compounds of these simple intervals. There are many implications to this seemingly minute detail, and in later installments, I'll share all of it.

What I want certain readers to realize, though, is that this ISN'T a "Russell had it wrong, don't waste your time on the LCC" kind of development. While disagreeing with Russell on some important points, I think that his theory, his system, and his approach, have some very important ideas and concepts that should not be discarded simply because other ideas may have been off-the-mark. To my detractors (you know who you are) I would say: be patient. Hear me out before you throw me out. Maybe wait a while to see where this is going before you pass judgement. You always have the option to ignore what I say.

All of the intervals in the preceeding discussion had a particular property or quality: they were all OVERTONAL, meaning they are all ratios that are present and prominent in the OS of the tonic.

There is another way that two tones can relate to one another, and a sort of prototype for all of this is the P4 interval. It occurs early in the OS, between partials 3 and 4, or between the perfect fifth and the octave. When a tone makes this interval to a lower tone, or bass note, it is both audibly and mathematically evident that something is different, even opposite, to what was heard and seen with the P5 interval. Rather than the lower tone being the "tonic", "generator", or "parent" of the upper tone, the reverse is true. The ratio is not found in the OS of the lower tone, but rather the lower tone has a nice spot in the OS of th upper tone. It has the opposite "polarity" if you will, to the P5 interval.

In the system of visually representing ratios and intervals that I discussed earlier, you would indicate this interval as a dot to the LEFT of the dot representing the tonic. It's a P5 BELOW the tonic.

P4 .... 1

Just like the overtonal ladder of fifths, you could draw a dot which represents a reciprocal 9th partial, 27th partial, etc.:

m3 .... m7 .... P4 .... 1

Mathieu calls intervals like this "reciprocals", rather than overtonals.

THIS was, I think, what Russell heard when juxtaposing Lydian with Major. The Lydian scale in any voicing, is ENTIRELY OVERTONAL, giving it a particular quality of unity with the tonic, since all of the intervals present exist within the tonic's OS. The P4, however, is NOT in that pattern. At least no where that makes a CLOSE relationship to the tonic. The P4 that is CLOSE to the tonic is a strong RECIPROCAL in the presence of otherwise overtonal intervals.

And just as there is a 5th partial in the OS, there is a reciprocal to that M3 interval: the m6.

1m6

Just as an entire lattice of overtonal intervals can be graphed, the same can be done with the reciprocals.

As you can see, there is more than one "version" for many of the intervals (there are even a few more if you observe the ratios made by the 7th partial).

So which one is the "right" one? This is an area where I make quite a departure from both Russell and Hindemith. It is my view that both of them (as well as this Delamont guy that joegold is versed in) had too strict a notion of what each interval "actually is" in ratio terms, and therefore had a too strict notion of what the interval root is.

Since there are two M6 intervals available, the 5:3 (close to tonic, but with a reciprocal component) and the 27:16 (entirely overtonal), each with a different POSTURE toward the tonic, the interval tonic is not the same for the two "versions". For the m3 interval, you have the Pythagorean reciprocal 32:27, you have the "close" 6:5 (reciprocal relative to the 3rd partial), and you have the entirely overtonal 75th partial (probably better named a #2). The interval tonic is not always the same.

So my point is that we should avoid a strict "a m3 is a m3 is a m3" notion (and the resulting 'interval tonic' designation), and instead, embrace the fact that an interval that we generally call a "minor third/augmented second" could have one of several available relationships with the tonic, even though the same key or fret on a 12TET instrument is used as a "reasonable stand-in" (to borrow joegold's term) for all of them.

In these cases, then, how do we know which version we're hearing, which one we're using? The answer is CONTEXT. Remember the 5th partial M3 and the 81st partial M3? Which one are you using? Which one are you hearing? I think that when you voice a chord like Russell's Lydian LADDER (that he used in the side-by-side comparison with Major), you have created a context where the M3 can be experienced as the 81st partial. It can be related to the tonic in a way suggested by the voicing. But when you play a major TRIAD, the ear will relate that M3 to the tonic by the "closest", most direct relationship that is available, the 5th partial.

In other words, the ear hears "CLOSE FIRST, UNLESS CONTEXT (in the form of other close intervals that bridge the gap) SUPPORTS A MORE DISTANT VERSION" of the interval. So, when you play a minor triad, the relationship of the m3 to the tonic will be the closest one available: the 6:5 version, where the third is a M3 reciprocal of the P5.

minor triad:

1 ... 5...... m3

When you play a diminished triad, however, the P5 is gone, and there is a o5, which is "close" to the pythagorean reciprocal version of m3.

diminished triad:

m3 ... () ... () ... 1...... 05

Add a M7 to this chord, and maybe that provides context to convert the other two tones to overtonal ones, the 45th and 75th partials.

dim triad w/ M7 added:

() ... #2() ... M7 ... #41 ... () ... ()

This is a logical "chapter two" to what preceeded it, introducing the reciprocal intervals, and the fact that intervals can have more than one "version", each with a different character.

I'm saying that over a C bass note, several intervals have an overtonal relationship with the C, as a result of being more or less "in tune" with partials of C's overtone series, thereby being a "unity" with the C, to use some Russell terminology.

This is one "class" of intervals, and they can range from 'ingoing' to 'outgoing', close to distant.

However, if you sing (and singing is more effective than playing for feeling the difference) an F over that C, you make them "in tune" by making the C occupy the position of 3rd partial in F's overtone series. In the perfect fourth interval, F is the 'daddy', so F is out of place, you could say, in the vertical presence of C D E G A B, since these are all overtonals. F# is more 'at one' with the C, because unlike F, it IS in the projected pattern of C's overtone series.

Intervals that relate to C in the manner that F does (putting C in THEIR overtone series), like Ab and Db (in which C is the 5th partial and 15th partial, respectively) have a particular quality about them, just as overtonal intervals have a particular quality about them - it's based on HOW they relate to the sounding tonic.

It's good to talk with someone who is familiar with the same material I have studied, and even much more.

I thank you for you frank honesty. I don't expect everyone, or even anyone, to agree with me, but at least when people don't it's good to know they have thoroughly considered what I have proposed, and truly disagree with it for reasons that make sense to them (as opposed to just putting up a wall, like some do).

I'm not sure how to reconcile some of your (Delamont's, actually) harmonic ratios, though. (I did look at your scanned PDF when you first posted it, but for some reason, I can't get the link to work anymore - I didn't see anything in it that added much to your distilled version here in the forum).

On the one hand, you said: "But what we musicians today all recognize as harmony, and especially harmonic progression, is a 5-limit affair. " (and that the 7th partial does not really figure in our sense of harmony, much less the higher partials)

But then, you cite frequency ratios representing not only the 7th partial, but the 11th as well. Your M7 interval, for example, you suggest as being 6:11 (as one possible version).

This idea, too, about distorted partials, I have a hard time with. I know it's all theoretical, and maybe no one can really "prove" how we actually respond to this stuff, but I still have to go by what seems reasonable to me.

By your reckoning, the M7th interval in a M7 chord could be a 'distorted' 7th partial. But when I compare a 7th chord with a M7 chord, I hear two distinct sonic structures, not an 'in tune' and an 'out of tune' version of the same chord.

And on a just-tuned intstrument, the tuning is based around three justly-tuned major triads, so the M7 chord would truly be the ratio of 8:10:12:15.

By your reckoning, the minor triad is just a major triad with a 'distorted' 5th partial. But if the 81st partial (pythagorean0 version of the M3 is too distant to be harmonious, how can a much more deviated ratio really represent the 5th partial?

There is clearly something RELATIVE, or RELATED about an A minor triad and a C major triad. To me, the thing they share in common is the 5:4 ratio between the C and E. This means that the minor third (C) in a minor triad does not relate directly to the tonic of the interval, A, but indirectly relates to A by first relating to E. C has a RECIPROCAL relationship to E by the 5th partial, much like F has a reciprocal relationship to C by the 3rd partial.

I agree that GR's notion of the tritone being passive is not quite right. (especially the Reed Gratz article, which does no more than prove that 6 times a number half of 12 times that number - not that relevant to harmony, just looking for a reason to prove Russell's Lydian vs. Major foundation).

I think the Church's banishment of the tritone was foolish, but calling the tritone consonant is just an over-reaction to that restriction. It's just another interval to use (it's not the devil), but it has a different relationship to the tonic than the P4 does. One of it's "versions" is overtonal (the 45:32 version), but distant. So, it's kind of 'out', in the sense of being related by a more complex ratio than the 'close' intervals, but it's also a "unity" with the tonic, being part of the tonic's OS. The P4 is kind of opposite, in that, despite being 'close' (related by a simple ratio 4:3), it is NOT present in the tonic's OS, but the tonic is part of ITS OS. So, it's 'close', but not a "unity" with the tonic, as Russell might put it.

You wrote: "The overtonal tritone is usually seen as involving the 11th partial, so 8:11. "

Again, I don't think we can just look at 'how high' the partial number is. Have you listened to the 11th partial, or even the 7th? The 13th partial is even worse. I can't see that a chord produced on any instrument, in any tuning, is "working" for us because of hinting at this partial. In isolation, a M6 interval just BEGS for a P4 to be added, because the simple ratio 5:3 is heard. Within a M13#11 chord, though, all intervals are overtonal, and the context would seem to place the M6 in a place that fits the overall pattern: 27th partial (pythagorean M6).

Having an "every interval has only ONE possible version" may be in the interests of 'simplifying' things, but IMO it only causes problems reconciling certain intervals in certain contexts. I think it's better to recognize and embrace the multiple identities that certain intervals can have. Like the M6, for example, having an 'alter-ego' in the 27th partial. 27 may seem like a 'high number', but it's mathematically simple: it's only one step higher in the pattern that you accepted in the 9th partial. While more 'distant' than the smaller 5:3 version, it fits in whth the overall harmonic pattern in larger contexts. Basically, in isolation or in the presence of a P4, we hear 5:3

You can't just look at a partial number, and say: "that's a high number, it's way out". The 512th partial is just a higher-octave statement of the fundamental. The 192nd partial is just a statement of the third partial (P5 interval). So, some partial numbers that appear high, actually have a pretty simple relationship with the tonic ( a short path to it, if you will). The 45th partial, for example, relates to the tonic as the 5th partial of the 9th partial, or the M3 of the M2. If the 44th partial were the tritone, it would equate with the 11th partial. To me, it seems that where possible, intevals will relate to the tonic, and to each other, by whatever combination of P5ths and M3rds is the 'shortest path'. They'll accept a less direct path if other tones create a context for this, but always by some combination of P5ths and M3rds. Not by the 11th or 13th partials. ( I actually make allowance for 7th-partial relations in some situations, but more later on that).

Anyway, I know Russell and Mathieu are coming from two different perspectives. But I truly see each as kind of speaking to shortcomings of the other. I'll go into more application and analysis soon. Thanks for chiming in, though. Maybe there's no real way, or even reason to, state conclusively whether the #4 is best represented by the (11th) 44th or 45th partial, but we each know where we stand on it, and why. I'd like to hear if others have an opinion, too.

I think there is a kind of "for" or "against" mentality when it comes to the LCC, as if one must accept all aspects of what is presented in the book(s) or else reject all of it. I think this has the effect that people who don't necessarily agree with or even understand the 'theory' part of it as Russell explains it (ladder of fifths, and all) defend the LCC as a whole, when what they really gained from the LCC is not theory at all, but a method of organization.

It's actually more than a method of organization. To me, one of the most valuable contributions of LCC is that it provides a NOMENCLATURE that equips one to freely and comfortably deal with scales and chords that deviate from the traditional major/minor and even the so-called 'Church' modes. Having a naming system for these things, you can feel free to USE them freely, rather than treating them as interesting oddities that don't really fit into the scheme of "real" music.

So, you have names for things that were kind of 'forbidden' before. Awesome. Thank you GR. But I ask you: Do you need a ladder to embrace and use this aspect of the LCC? If you became an advocate of the LCC because of the powers that it's nomenclature placed in your hands, does that oblige you to agree with the ladder of fifths THEORY even if there are aspects of the theory that are a bit hard to reconcile? Do you accept those 'hard to reconcile' bits because you came to UNDERSTAND them, and they now make perfect sense to you, or because they seem to not really matter, since the SYSTEM and its nomenclature are benefiting you, and that's enouph?

One objection that some raise to learning the LCC is "why do I have to re-learn everything I already know and now call it 'lydian-this' and 'lydian-that'?" I don't personally object to learning new names, but I know many do, and it's a legitimate point.

So I will ask a question: Is it necessary to re-learn everything from the lydian tonic perspective in order to reap the benefits that LCC's nomenclature bring?

Before LCC, modes were still a part of the music theory/education canon, and were referred to (still are by those not versed in LCC) as "Dorian", "Aeolian", "Mixolydian" , and so on - the "Church modes" if you don't mind the term. Is there any reason "Lydian Diminished MG VI" could not be called "Dorian flat fifth" or something like that? In other words, rather than calling everything "Lydian (whatever), MG (whatever)", just call the mode by the name that most people are already used to, and after that, mention the degree that is altered.

Every vertical structure that can be described using LCC nomenclature can just as well be described using the above approach to naming. They are equal. Kind of. What's the difference? They each reflect a slightly different priority.

The LCC, by virtue of it's underlying ladder theory, gives priority to the "Lydian Tonic" as a tone that must be considered as the objective reference point for everything. In the next breath, of secondary concern, is the Modal Genre, from which you can determine the actual Modal Tonic.

If you wanted the empowerment of an expanded nomenclature, but did not really go for the underlying lydian ladder thing, you would place priority on naming first the LETTER NAME of the TONIC on which you're going to sound a chord or scale or whatever. After stating the tonic name, in the next breath you name Modal Genre, but call it by the traditional mode name. For me, and I would assume many a musician, the mere mention of "Dorian", "Phrygian", or whatever, INSTANTLY conveys the needed information - namely, the six intervals that this mode makes to the tonic, and the feeling or colour, that will result. Having that starting point, you can then easily modify a member of the mode.

What would be gained, and what would be lost, by using this approach to nomenclature as opposed to the LCC approach?

Well, a gain would be the immediacy of what to many, is the most significant peice of information: the tonic's name. Another is the immediacy of the intervals that the mode name suggests (not really a benefit if you didn't know the modes well already, though). Another is an immediate recognition of the interval TO THE SOUNDING TONIC that is being altered. Another is, again, not having to 're-learn' what you already know with different names (not a problem if introduced to LCC before even modes, but this is an unlikely scenario).

Some losses: You would lose the immediate sense of commonality betweeen 'A Dorian', 'E Aeolian', 'B Phrygian' and the other four modes that share this common pool of notes. That would be pushed into the periphery as a less important peice of information (rightly or wrongly). You would lose the immediacy of the "Lydian Tonic Interval", and the measurement of what interval the "altered note" makes to the Lydian Tonic. This is only a loss, though, if you conisider this measurement to be an important one. (my approach is to instead reconcile all intervals with the sounding tonic).

The LCC, as I see it, names things this way: "Quality first, place second" (since you have to 'figure out' what tonic you're on, or if you know that, you have to figure out what the parent scale is). The naming convention I am proposing above, is more in keeping with that of chord nomenclature, and even classical analysis, and that is: "Place first, Quality second".

For me, I first want to know where I am, what note I'm sitting on as the 'root'/'tonic' (I'm aware that some have issues with the generality of those terms). Next, I want to know what intervals to sound along with that tonic, and thereby know what quality or effect I'm going to project. To me, this is more intuitive than the LCC approach to nomenclature, yet is capable of capturing any verticality that LCC can. Some things are lost along the way, some are gained. It depends on what is important to you as a musician and what kind theoretical model makes the most sense to you (since none are 100% verifiable and will always carry the term "theory").

This nomenclature point is a kind of "Chapter 3" in this discussion of my "alternative take on underlying theory". Feel free to weigh in, comment, agree, disagree, whatever.

Why? I already knew you were a smart, well schooled guy who could play.

But what you have above so many other "objectors" is that - while not finding an incontrovertible explanation to immediately satisfy your own line of questioning - you have an open mind enough to see some of what IS here.

Great post. I agree totally that it's not just different names for the same things. If you lose the nomenclature and the rationale (however mysterious or unexplained), you lose information.

Check out p. 148 of you haven't yet. I prefer to call it Lydian #2, but the book says Lydian b3. I guess it keeps the 9th open for use.

Forgive me if someone has mentioned this: the harmonic minor is considered a horizontal scale in the LCC. If you think about it, a harmonic minor sounds great resolving to a minor tonic station but wouldn't be the best choice, or my best choice once I arrived there.

i agree that the concept need not be an all or nothing proposition. good conversation; carry on...

i also agree with much in the previous posts; far too numerous to quote, but in particular that something is lost when viewing the concept as merely a renaming of modes and other materials...

one thing i really like about the concept is the emphasis on lydian tonics as guide tones (also as prominent chord tones) for tonal expansion rather than the roots of chords, which seems to have reduced the required number of "member scales" quite drastically. there is so much more to this that i would like to post in the future but you guys seem to be hitting on the major points...

as to the harmonic minor issue, it shows up in the form of the major augmented fifth, a horizontal scale as guitarjazz pointed out. i think the lydian #2 makes for a great official scale for this purpose as well...

joegold wrote: "Yet later on in your post you seem to be reject that nomenclature. Hmm. "

It's not so much a REJECTION of the nomenclature, as an allowance that all the structures that can be described with LCC nomenclature can be described otherwise. So if someone thought that LCC puts chords/scales in their hands that were inconceivable otherwise, that's not entirely true. I started another post called "Pool of Tangible Benefits" in which I asked for examples of chords that the Concept provides that were not previously available and not one person provided one. I expected that, actually.

joegold wrote: "But without the idea that the tonic of Fred is the centre of the vertical organization of the chord - the Concept, its methods and its results would be seriously diluted. "

You'll note that I specifically acknolwedged what is lost when naming stuff relative to the Modal Tonic rather than the Lydian Tonic. I agree it's a trade-off, I'll be exploring the benefits gained in that trade-off shortly. But you definitely do lose something, I'm not disputing that.

joegold wrote: "But within this process I'll be missing out on many of the most important facets of the LCC and several of the hipper-sounding chord-scale alliance suggestions that the LCC makes would be available only as super-impositions or reharms, as described above. "

So what are some examples of sounds that ONLY the LCC perspective would yeild?

Anyway, one of the goals of my 'alternative viewpoint on theory' is to equip myself and any one who is interested, with a less "chord-family" -centred approach, and more of an organic, 'sum-of-it's-intervals' approach, recognizing the basic qualities of intervals that relate to a tonic overtonally versus those that relate to it reciprocally. I find that the strict chord-family approach is what has it's limits, and cannot explain certain things.

For example, the only scales offered in LCC to cover the 11-tone order and 12-tone order (I realize these are just the suggested best REPRESENTATIVES of those tonal orders) are the AD and ADB scales - actually the same scale, just as LA and Lb7 are. In AD and ADB, there is NO difference between MGI, MGVI and MG+IV. So, at some point, MG ceases to be a meaningful point-of-reference.

I think if you look at harmonic structures as collections of intervals, each of which we can get aquainted with individually, the "morph" between the otherwise distinct "modal genres" is a little more organic and fluid. That's what I'm aiming for - a less "scale-and-chord"-driven scheme, and more of a "get to know the OS and the intervals it posesses" thing.

dogbite wrote: "merely a renaming of modes and other materials... "

No, I get how LCC is more than that. It's just, I see each tone's interval with the SOUNDING TONIC (including the "out note" of a scale) as being more significant than it's interval with the LYDIAN TONIC, so I have tweaked the nomenclature to reflect that, even though the naming efficiency is now lost.

Joegold: I thought for a long time about the chord-scale options you proposed above, and, you're right: LCC is the only chord-scale system that would provide these choices. I'ts probably the only means, period, by which most musicians would arrive at these combinations.

I've been thinking a lot about the similarities and differences between the various approaches to examining harmony. Something that is clear about stretching tonal harmony, whether you reckon the structure using a Pythagorean kind of model, or more of a 5-limit system (like I do), is this:

At some point, reaching "up" results in intervals that are very close to those obtained by reaching "down". The closeness leads us to treat the two "versions" as the same interval, and consider anything beyond the most distinct intervals as redundant. This is what leads to the 12 in a 12-tone system. There are 12 intervals that are really distinct from each other, and the finer variances seem to overcomplicate matters (for some, anyway). That's why some have expressed thankfulness for 12TET, in that it saves you from worrying about those minute variances and just get on with using what seems to be natures's promoted candidates.

I think what I've learned from my time on the forum is that, while I consider a closer examination of the OS' partials interesting and relevant, and consider Russell's angle on such things to fall short of the scientific soundness he claimed, most people don't really care about these things, and refer to them as "minutiae". AND THAT"S OK.

I think it is universally agreed in here that Russell came up with an elegant, powerful, and unique system of organization. It's a chord-scale system, but it's more than that. Anyone who can put within your grasp complex chordal structures, while at the same time simplifying the amount of information you need to pay attention to at any given time has accomplished something amazing. Anyone who can come up with that AND share it with the world is more amazing still.

Mrs. Russell is right. No one here should be put in the position of defending the Concept. Yet I know that all this "alternative viewpoint" stuff kind of puts people in that position.

Regardless of theoretical underpinnings, and any advantages gained by considering such, the net result is what this forum is here to celebrate and explore. So, while I will certainly continue my tangents and disoveries "under the hood", and continue to recognize what I consider strengths and weaknesses of Russell's argumentation, I will not be posting these things on the forum from now on. I know the LCC lingo, and I see the advantages - so my future participation will be limited to the forum's intent. If you have any questions about what I've posted in this thread, by all means send me a PM, but as for the forum, I don't want to burden it with 'baggage from the outside'.

I read the linked articles, and get your point. I'm also encouraged that you would "beg" me to read them. You obviously see something valuable in what I've been developing and posting.

quote from Einstein in your linked article: "None of these three points can rank as a logical objection against the theory. They form, as it were, merely unsatisfied needs of the scientific spirit in its effort to penetrate the processes of nature by a complete and unified set of ideas."

Tone = I can identify gaps and shortcomings without opposing or belittling the man or his ideas. Profound awe does not require deification.

Agreed, and thanks for the advice. I know I've overstepped this balance a time or two (remember the "Down with the Ladder" thing?).

The multimedia stuff is a suggestion I've brushed off too many times, too, so thanks for stressing that as well.

There are several intervals that fall within the space of what we generally refer to as the "Perfect Fourth". The first one encountered in the OS is between partials 3 and 4 , the "4:3" ratio, where the upper note is 1.333333 times the frequency of the lower note. 498 cents in ET terms. This one is obtained basically by reaching "down" instead of up into the OS..

A second "version" if you will, is what you get when you continue the Pythagorean "ladder" to the 12th tone in the ladder. Partial numbers are too high to be very meaningful. The lower note is 1.3515244 times the frequency of the lower note. 522 cents in ET terms. This one is obtained by reaching "up" into the OS.

A third version is also obtained by reaching up, but is much 'closer to earth' than that pythagorean one. It's a fifth above the 7th partial, or the 21st partial (7x3=21) in other words. The ratio is 1.3125, and the ET value is 470 cents.

Anyway, that's getting a bit more thorough than needed to answer your question. For every interval (let's stick to {Pythagorean intervals for a moment) obtainable by stacking fifths up, there is another "version" 23 cents smaller obtained by stacking fifths down. Again, not suggesting 'undertones' or anything, just giving frequency ratios.

Stacking up gives us 11 unique intervals, but when we go for the 12th interval, we have a tone only 23 cents away from the starting tone, and it sounds like an "out-of-tune" version of the octave. I'm not sure anyone has a 100% objective historical take on where and when 12 was arrived at as the most manageable number of tones, but the above is most certainly at the heart of it.

joegold wrote: "If his theories are valid it is much more than just a chord-scale-system."

Even if his theories are not valid, he still opened the door to a much wider view of "tonal resources" than previsouly known or encouraged.

joegold wrote: ""Simplifying"? Hardly."

Well, although it's quite a tall order to get to the point of THINKING in terms of lydian tonic in all situations, if you can get to that point, your job is simpler, I'd say.

joegold wrote: "I hope you'll reconsider."

Thank you for this, really. If it were only forum members expressing irritation at my ramblings, I'd certainly press on. However, I think since Mrs. Russell is footing the bill for this site (and with some reluctance at that), I don't think anything that could be used to "disprove" Russell's theory is best posted here. Maybe you'll see a book on the stands in a few years, who knows? ( and I dont' mean a "why the LCC is dead wrong" book, either)

joegold wrote: "If the LCC can not survive any "baggage from the outside", then it will not survive. IMO."